| On Semiclean Group Rings |
| Received:December 07, 2015 Revised:December 02, 2016 |
| Key Words:
clean ring semiclean ring group ring locally finite group
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11401009) and the Natural Science Foundation of Ahui Province (Grant No.1408085QA01). |
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| Abstract: |
| A ring $R$ with unity is called semiclean, if each of its elements is the sum of a unit and a periodic. Every clean ring is semiclean. It is not easy to characterize a semiclean group ring in general. Our purpose is to consider the following question: If $G$ is a locally finite group or a cyclic group of order 3, then when is $RG$ semiclean? Some known results on clean group rings are generalized. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2017.02.007 |
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